MATHEMATICAL STUDIES ON SEARCH PROBLEMS ON GRAPHS

1.Kikuta和w.h.l uckle教授一直在共同研究积累游戏，这是一类检验游戏。1999年10月至2000年5月，他在神户商业大学担任客座教授。在此期间，菊田和拉克尔教授共同研究了搜索游戏等。由于积累博弈领域存在许多问题（参见《积累博弈，第1部分：噪声搜索》第396页的表1）。《最优化理论与应用学报》1997年第94卷（作者：Kikuta和Ruckle），这项联合工作将继续下去。2000年9月，巴斯顿在神户商业大学做了10天的客座教授。Kikuta和Dr.Baston共同研究了集合搜索问题，找到了对称标记开始集合搜索情况下的最优策略和最优值。这项联合工作目前仍在继续。Kikuta一直在研究有限图上有旅行代价的搜索博弈问题，最近解决了底层图为循环图且参数满足一定条件时的搜索博弈问题。这个研究还在继续，为了解决一般的循环图上的一个博弈，弗格森教授对这个研究进行了评论。Kikuta， Hamada和Kiniwa一直在分析搜索游戏，这与一些仲裁系统的探测复杂性有关。当底层网络呈轮状时，博弈已经解决（关于某些仲裁系统的探针复杂性，mimeo）。1999年4月，菊田、金羽和滨田)。对其他情况的分析仍在继续。

1.Kikuta and Prof.W.H.Ruckle have been studying jointly on Accumulation Games, which are a class of inspection games. Prof.Ruckle stayed at the Kobe University of Commerce as a visiting professor from October, 1999 to May, 2000. During his stay, Kikuta and Prof.Ruckle studied jointly on search games etc. Since there are many problems in the area of accumulation games (Table 1 at page 396 of [Accumulation Games, Part 1 : Noisy Search.Journal of Optimization Theory and Applications, Vol.94, 1997 by Kikuta and Ruckle], this joint work would continue.2.Dr.Baston stayed at the Kobe University of Commerce as a visiting professor about ten days in September, 2000. Kikuta and Dr.Baston studied jointly on Rendezvous Search, and found optimal strategies and the optimal value for the case of symmetric markstart rendezvous search. This joint work is now in continuation.3.Kikuta has been studying on search games with traveling cost on finite graphs, and recently solved the game when the underlying graph is a cyclic one and the parameters satisfy some condition. This study is still in continuation, for solving generally a game on a cyclic graph.Prof.Ferguson gave comments on this research.4.Kikuta, Hamada and Kiniwa have been analyzing search games, related to the probe complexity of some quorum systems. When the underlying netwok is wheel-shaped, the game had been already solved (On probe complexity of some quorum systems, mimeo. April, 1999, by Kikuta, Kiniwa and Hamada). Analysis in the other cases is still in continuation.